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Line A has a slope of 3/2 and passes through the point (3, 3). Line B has a slope of – 1/3 and passes through the point (-4, -2). At what point does line A intersect line B? Line Aintersects line B at the point ( , ).​

Sagot :

Sreedevi102idn

Answer:

The lines meet at (-1, -3)

Step-by-step explanation:

Line A :

[tex](x_1, y_1) = (3, 3) \ ; \ slope, \ m_A = \frac{3}{2}\\\\Equation \ of \ line \ A : (y - 3) = \frac{3}{2}(x - 3)[/tex]

                             [tex]2(y - 3) = 3(x-3)\\2y - 6 = 3x - 9\\2y = 3x - 9 + 6\\2y = 3x -3[/tex]

Line B :

[tex](x_2,y_2) = (-4, -2) \ ; \ slope , m_B = -\frac{1}{3}\\\\Equation \ of\ line \ B: (y -(-2)) = -\frac{1}{3}(x -(-4))[/tex]

                             [tex]3(y + 2) = -1(x+4)\\3y + 6 = -x -4\\3y = -x - 4 - 6 \\3y = -x - 10[/tex]

Solve for x and y from the linear equation to find where line A and line B meets :

2y = 3x - 3 => 3x - 2y = 3 ------- (1)

3y = -x - 10 => -x = 3y + 10

                => x = - 3y - 10 --------(2)

Substitute (2) in (1) : => 3(- 3y - 10) - 2y = 3

                                   -9y - 30 -2y = 3

                                       -11y = 3 + 30

                                         -11y = 33

                                            y = -3

Substitute y in (2) : => x = -3 (-3) - 10 = 9 - 10 = -1

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